Spaces of geometrically generic configurations

2006/01/14 by Yoel Feler, Feler, Yoel
Mathematics · #14J50 #32H02 (Primary) 32H25 #32M99 (Secondary) #Algebraic Geometry (math.AG) #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Mathematics and Applications #Meromorphic and Entire Functions #math.AG #math.CV #msc:14J50 #msc:32H02 #msc:32H25 #msc:32M99

paper · pdf · doi:10.48550/arxiv.math/0601362

31 pages

arxiv created 2006/01/14 · openalex publication_date 2006/01/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X denote either CP^m or C^m. We study certain analytic properties of the space Eⁿ of ordered geometrically generic n-point configurations in X. This space consists of all q=(q₁,...,q_n) in Xⁿ such that no m+1 of the points q₁,...,q_n belong to a hyperplane in X. In particular, we show that for X=CP^m and n big enough any holomorphic map f:Eⁿ-->Eⁿ commuting with the natural action of the symmetric group S(n) in Eⁿ is of the form f(q)=t(q)q=(t(q)q₁,...,t(q)q_n), for q in Eⁿ, where t:Eⁿ-->PSL(m+1,C) is an S(n)-invariant holomorphic map. A similar result holds true for mappings of the space of ordered geometrically generic n-point configurations in C^m.

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